Direct recovery of interfacial topography from coherent X-ray reflectivity: model calculations for a 1D interface
The use of coherent X-ray reflectivity to recover interfacial topography is described using model calculations for a 1D interface. The results reveal that the illuminated topography can be recovered directly from the measured reflected intensities. This is achieved through an analysis of the Patterson function, the Fourier transform of the scattering intensity (as a function of lateral momentum transfer, Q//, at fixed vertical momentum transfer, Qz). Specifically, a second-order Patterson function is defined that reveals the discrete set of separations and contrast factors (i.e. the product of changes in the effective scat...
Source: Acta Crystallographica Section A - May 31, 2020 Category: Chemistry Authors: Fenter, P. Tags: coherent reflectivity surface topography phase problem research papers Source Type: research
Sets, Groups, and Mappings. An Introduction to Abstract Mathematics. By Andrew D. Hwang. American Mathematical Society, Pure and Applied Undergraduate Texts No. 39, 2019. Hardcover, pp. xv+304. Price USD 82.00. ISBN 9781470449322
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - May 19, 2020 Category: Chemistry Authors: Nespolo, M. Tags: book review group theory book reviews Source Type: research
Extending the Debye scattering equation for diffraction from a cylindrically averaged group of atoms: detecting molecular orientation at an interface
The Debye scattering equation is now over 100 years old and has been widely used to interpret diffraction patterns from randomly oriented groups of atoms. The present work develops and applies a related equation that calculates diffraction intensity from groups of atoms randomly oriented about a fixed axis, a scenario that occurs when molecules are oriented at an interface by the presentation of a binding motif as in antibody binding. Using an example biomolecule, the high level of sensitivity of the diffraction pattern to the orientation of the molecule and to the direction of the incident beam is shown. The use of the me...
Source: Acta Crystallographica Section A - May 19, 2020 Category: Chemistry Authors: Ross, A.E. McCulloch,D.G. McKenzie, D.R. Tags: Debye scattering equation diffraction biomolecules orientation modelling research papers Source Type: research
Isotopy classification of three-dimensional embedded nets
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - April 28, 2020 Category: Chemistry Authors: Schulte, E. Tags: embedded nets isotopy classification topology scientific commentaries Source Type: research
The Fedorov – Groth law revisited: complexity analysis using mineralogical data
The Fedorov – Groth law points out that, on average, chemical simplicity corresponds to higher symmetry, and chemically complex compounds usually have lower symmetry than chemically simple compounds. Using mineralogical data, it is demonstrated that the Fedorov – Groth law is valid and statistically meaningful, when chemical complexity is expressed as the amount of Shannon chemical information per atom and the degree of symmetry as the order of the point group of a mineral. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - April 27, 2020 Category: Chemistry Authors: Krivovichev, S.V. Krivovichev, V.G. Tags: symmetry chemical composition complexity Shannon information Fedorov – Groth law short communications Source Type: research
New kind of interference in the case of X-ray Laue diffraction in a single crystal with uneven exit surface under the conditions of the Borrmann effect. Analytical solution
The analytical solution of the problem of X-ray spherical-wave Laue diffraction in a single crystal with a linear change of thickness on the exit surface is derived. General equations are applied to a specific case of plane-wave Laue diffraction in a thick crystal under the conditions of the Borrmann effect. It is shown that if a thickness increase takes place at the side of the reflected beam, the related reflected wave amplitude is calculated as a sum of three terms, two of which are complex. If all three terms have a comparable modulus, it can lead to an increase in the reflected beam intensity by up to nine times due t...
Source: Acta Crystallographica Section A - April 27, 2020 Category: Chemistry Authors: Kohn, V.G. Smirnova, I.A. Tags: X-ray diffraction topography intensity increase effect uneven exit surface single crystals research papers Source Type: research
Domain formation and phase transitions in the wurtzite-based heterovalent ternaries: a Landau theory analysis
Characterizing the crystalline disorder properties of heterovalent ternary semiconductors continues to challenge solid-state theory. Here, a Landau theory is developed for the wurtzite-based ternary semiconductor ZnSnN2. It is shown that the symmetry properties of two nearly co-stable phases, with space groups Pmc21 and Pbn21, imply that a reconstructive phase transition is the source of crystal structure disorder via a mixture of phase domains. The site exchange defect, which consists of two adjacent antisite defects, is identified as the nucleation mechanism of the transition. A Landau potential based on the space-group ...
Source: Acta Crystallographica Section A - April 27, 2020 Category: Chemistry Authors: Quayle, P.C. Tags: Landau theory phase transitions antiferroelectrics crystalline disorder properties heterovalent ternary semiconductors research papers Source Type: research
Structure-mining: screening structure models by automated fitting to the atomic pair distribution function over large numbers of models
A new approach is presented to obtain candidate structures from atomic pair distribution function (PDF) data in a highly automated way. It fetches, from web-based structural databases, all the structures meeting the experimenter's search criteria and performs structure refinements on them without human intervention. It supports both X-ray and neutron PDFs. Tests on various material systems show the effectiveness and robustness of the algorithm in finding the correct atomic crystal structure. It works on crystalline and nanocrystalline materials including complex oxide nanoparticles and nanowires, low-symmetry and locally d...
Source: Acta Crystallographica Section A - April 27, 2020 Category: Chemistry Authors: Yang, L. Juh á s, P. Terban, M.W. Tucker, M.G. Billinge, S.J.L. Tags: pair distribution function PDF automated fitting atomic structure structure discovery research papers Source Type: research
Wedge reversion antisymmetry and 41 types of physical quantities in arbitrary dimensions
It is shown that there are 41 types of multivectors representing physical quantities in non-relativistic physics in arbitrary dimensions within the formalism of Clifford algebra. The classification is based on the action of three symmetry operations on a general multivector: spatial inversion, 1, time-reversal, 1 ′ , and a third that is introduced here, namely wedge reversion, 1 † . It is shown that the traits of `axiality' and `chirality' are not good bases for extending the classification of multivectors into arbitrary dimensions, and that introducing 1 † would allow for such a classification. Since physical proper...
Source: Acta Crystallographica Section A - April 27, 2020 Category: Chemistry Authors: Gopalan, V. Tags: multivectors wedge reversion antisymmetry Clifford algebra research papers Source Type: research
Testing of a `hard' X-ray interferometer for experimental investigations
A `hard' X-ray LLL interferometer is tested for experimental investigations. The interferometer has both a base and a `ceiling', which are rigidly connected through columns. As a result, the interferometer does not have uncontrollable preliminary moir é . The intensity distribution is uniform in the interfering beams. It is shown that the interferometer is very sensitive to minor mechanical stresses. As a result, the interferometer must be freely placed on the goniometer head. Constant-thickness fringes are obtained using a wedge with a vertically placed apex. The volumes available for specimen placement are limited due t...
Source: Acta Crystallographica Section A - April 15, 2020 Category: Chemistry Authors: Eyramjyan, T.H. Mesropyan, M.H. Mnatsakanyan, T.S. Balyan, M.K. Tags: X-rays LLL interferometer `hard' LLL interferometer moir é fringes research papers Source Type: research
Multiple Bragg reflection by a thick mosaic crystal. II. Simplified transport equation solved on a grid
The generalized Darwin – Hamilton equations [Wuttke (2014). Acta Cryst. A70, 429 – 440] describe multiple Bragg reflection from a thick, ideally imperfect crystal. These equations are simplified by making full use of energy conservation, and it is demonstrated that the conventional two-ray Darwin – Hamilton equations are obtained as a first-order approximation. Then an efficient numeric solution method is presented, based on a transfer matrix for discretized directional distribution functions and on spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflect...
Source: Acta Crystallographica Section A - April 15, 2020 Category: Chemistry Authors: Bornemann, F. Li, Y.Y. Wuttke, J. Tags: mosaic crystals multiple scattering Darwin – Hamilton equations spectral collocation research papers Source Type: research
SPIND-TC: an indexing method for two-color X-ray diffraction data
Recent developments of two-color operation modes at X-ray free-electron laser facilities provide new research opportunities, such as X-ray pump/X-ray probe experiments and multiple-wavelength anomalous dispersion phasing methods. However, most existing indexing methods were developed for indexing diffraction data from monochromatic X-ray beams. Here, a new algorithm is presented for indexing two-color diffraction data, as an extension of the sparse-pattern indexing algorithm SPIND, which has been demonstrated to be capable of indexing diffraction patterns with as few as five peaks. The principle and implementation of the t...
Source: Acta Crystallographica Section A - April 1, 2020 Category: Chemistry Authors: Li, X. Li, C. Liu, H. Tags: serial crystallography two-color diffraction indexing algorithm research papers Source Type: research
Geometric realizations of abstract regular polyhedra with automorphism group H3
A geometric realization of an abstract polyhedron {\cal P} is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Γ . The method entails finding a real orthogonal representation of Γ of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H3. (Source: Acta ...
Source: Acta Crystallographica Section A - April 1, 2020 Category: Chemistry Authors: Aranas, J.A.L. Loyola, M.L. Tags: abstract regular polyhedra geometric realizations non-crystallographic Coxeter group H3 string C-groups research papers Source Type: research
An efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films
Crystal structure identification of thin organic films entails a number of technical and methodological challenges. In particular, if molecular crystals are epitaxially grown on single-crystalline substrates a complex scenario of multiple preferred orientations of the adsorbate, several symmetry-related in-plane alignments and the occurrence of unknown polymorphs is frequently observed. In theory, the parameters of the reduced unit cell and its orientation can simply be obtained from the matrix of three linearly independent reciprocal-space vectors. However, if the sample exhibits unit cells in various orientations and/or ...
Source: Acta Crystallographica Section A - April 1, 2020 Category: Chemistry Authors: Simbrunner, J. Schrode, B. Domke, J. Fritz, T. Salzmann, I. Resel, R. Tags: epitaxy indexing mathematical crystallography research papers Source Type: research
Groupoid description of modular structures
Modular structures are crystal structures built by subperiodic (zero-, mono- or diperiodic) substructures, called modules. The whole set of partial operations relating substructures in a modular structure build up a groupoid; modular structures composed of identical substructures are described by connected groupoids, or groupoids in the sense of Brandt. A general approach is presented to describe modular structures by Brandt's groupoids and how to obtain the corresponding space groups, in which only the partial operations that have an extension to the whole crystal space appear. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - April 1, 2020 Category: Chemistry Authors: Nespolo, M. Souvignier, B. St ö ger, B. Tags: modular crystal structures groupoids subperiodic groups superposition structures polytypism research papers Source Type: research
